Complex Permittivity Measurements of Substrates and Thin Films at Millimeter-wave Frequencies

Dielectric properties (i.e., relative permittivity and loss tangent) are key inputs for the design and modeling of devices. The importance and the difficulty of reliably measuring these properties increase as we move to higher frequencies, e.g. millimeter-wave (30 GHz – 300 GHz). Here, we show the use of split-cylinder resonators and fused silica substrates to develop SI-traceable standards for these properties. We describe the electromagnetic theory, uncertainty analysis, and limitations of split-cylinder resonator measurements. We then extend these split-cylinder resonator measurements from the simple case of homogeneous substrates to the more complicated case of thin films (ranging from ceramics like AlN to polymers like SU-8) on substrates. We extend the theory, uncertainty analysis, and the limitations of this more complicated case. This work allows us to deliver reliable material measurements of homogeneous substrates and heterogeneous material stacks with applications across the electronics industry.